It turns out it didn't take me long at all to catch up with Sword Art Online. Perhaps it's because I already read through the corresponding portions of the light novel, but I found the show much less objectionable on a whole than most of its critics. The biggest complaints I see tend to fall into two categories. First, Kirito is accused of being a "Mary Sue," and second, Asuna is characterized as too compliant or unassertive or lacking independence. I agree there is merit to these complaints in that the factors exist, but I'm not convinced they qualify as reasonable concerns to care about.
With regard to Kirito's "Mary Sue" qualities, it's true he has the abnormally good fortune of being better at basically everything than anyone else he encounters in the game, but that doesn't especially bother me. I guess anime has bombarded me with so many incompetent, weak-ass milquetoasts that even a potato with good stats is preferable to average spuds. So I don't care if Kirito's battles are tensionless because I know no real harm will to come to him. Other lead characters in various television shows and movies have plot armor too; he's no different.
So what about Asuna? I guess as Primary Love Interest she doesn't get much opportunity to do much except carve up chumps and soy sauce the shit out of some fish, but nobody else does much when Kirito is around either. So to me, the criticism about Asuna's contributions aren't so much directed at Asuna, but more towards that first issue regarding Kirito again. At least Asuna doesn't spend all her time being wined, dined, and supined, despite being Primary Love Interest—a genuine concern given that Kirito not only has the mysterious pull of a harem comedy protagonist, but also the willingness to pick a Best Girl and go with her. Given my track record for lamenting about the notoriously asexual proclivities of ostensibly male anime protagonists as a whole, I'm all right with giving a pass to one of their main squeezes even if she's best remembered for shacking up with one of them. It can't be helped.